The standard definition of atomicity—the thesis that everything is ultimately composed of entities that lack proper parts—is satisfied by a model that is not atomistic. The standard definition is therefore an incorrect characterization of atomicity. I show that the model satisfies the axioms of all but the strongest mereology and therefore that the standard definition of atomicity is only adequate given some controversial metaphysical assumptions. I end by proposing a new definition of atomicity that does not require extensionality or unrestricted (...) summation. (shrink)

Judaism is often described as a religion that tolerates, even celebrates arguments with God. In Pious Irreverence, Dov Weiss has written the first scholarly study of the premodern roots of this distinctively Jewish theology of protest, examining its origins and development in the rabbinic age (70 CE-800 CE).

From the point of view of non-classical logics, Heyting's implication is the smallest implication for which the deduction theorem holds. This book studies properties of logical systems having some of the classical connectives and implication in the neighbourhood of Heyt ing's implication. I have not included anything on entailment, al though it belongs to this neighbourhood, mainly because of the appearance of the Anderson-Belnap book on entailment. In the later chapters of this book, I have included material that might be (...) of interest to the intuitionist mathematician. Originally, I intended to include more material in that spirit but I decided against it. There is no coherent body of material to include that builds naturally on the present book. There are some serious results on topological models, second order Beth and Kripke models, theories of types, etc., but it would require further research to be able to present a general theory, possibly using sheaves. That would have postponed pUblication for too long. I would like to dedicate this book to my colleagues, Professors G. Kreisel, M.O. Rabin and D. Scott. I have benefited greatly from Professor Kreisel's criticism and suggestions. Professor Rabin's fun damental results on decidability and undecidability provided the powerful tools used in obtaining the majority of the results reported in this book. Professor Scott's approach to non-classical logics and especially his analysis of the Scott consequence relation makes it possible to present Heyting's logic as a beautiful, integral part of non-classical logics. (shrink)

Paul (Noûs 36:578–596, 2002; Noûs 40:623–659, 2006, The Handbook of Mereology, forthcoming) has argued for a bundle theory of objects that analyzes the bundling relation between properties and objects in terms of parthood relations. In this paper I argue that any mereological bundle theory with the explanatory power of Paul’s theory will entail the principle of the identity of indiscernibles (PII). This is problematic, since similar bundle theories seem to fall to Max Black’s two sphere counterexample to (PII). I argue, (...) however, that a fully developed mereological bundle theory provides a new way of interpreting Black’s two sphere universe that dispels the counterexample. I argue that this solution to Black’s puzzle is superior to other solutions on offer, and consequently that mereological bundle theory is an attractive ontological strategy for friends of (PII). (shrink)

This superb collection of papers focuses on a fundamental question in logic and computation: What is a logical system? With contributions from leading researchers--including Ian Hacking, Robert Kowalski, Jim Lambek, Neil Tennent, Arnon Avron, L. Farinas del Cerro, Kosta Dosen, and Solomon Feferman--the book presents a wide range of views on how to answer such a question, reflecting current, mainstream approaches to logic and its applications. Written to appeal to a diverse audience of readers, What is a Logical System? will (...) excite discussion among students, teachers, and researchers in mathematics, logic, computer science, philosophy, and linguistics. (shrink)

Inductive Logic is number ten in the 11-volume Handbook of the History of Logic. While there are many examples were a science split from philosophy and became autonomous (such as physics with Newton and biology with Darwin), and while there are, perhaps, topics that are of exclusively philosophical interest, inductive logic — as this handbook attests — is a research field where philosophers and scientists fruitfully and constructively interact. This handbook covers the rich history of scientific turning points in Inductive (...) Logic, including probability theory and decision theory. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in the history of logic, the history of philosophy, and any discipline, such as mathematics, computer science, cognitive psychology, and artificial intelligence, for whom the historical background of his or her work is a salient consideration. (shrink)

The present collection of essays honours John Woods on the occasion of his eightieth birthday from contributors who wish to pay homage to this remarkable researcher whom they see not only as a scholar of prodigious energy and insight, but as a friend, colleague, collaborator, or former teacher. All of the essays touch upon topics Woods has taken a direct or indirect interest in, ranging from technical problems of mathematical logic and applications of formal methods through philosophical logic, philosophy of (...) language, epistemology and history of ancient and modern logic. The sections themselves of the book cover relevance, paradoxes, inconsistency, fallacies, abduction, fictions, logic naturalized, law, argumentation and narratives, and many other topics: and represent the main research areas which have profited from Woods' reflections. (shrink)

Modal logics, originally conceived in philosophy, have recently found many applications in computer science, artificial intelligence, the foundations of mathematics, linguistics and other disciplines. Celebrated for their good computational behaviour, modal logics are used as effective formalisms for talking about time, space, knowledge, beliefs, actions, obligations, provability, etc. However, the nice computational properties can drastically change if we combine some of these formalisms into a many-dimensional system, say, to reason about knowledge bases developing in time or moving objects. To study (...) the computational behaviour of many-dimensional modal logics is the main aim of this book. On the one hand, it is concerned with providing a solid mathematical foundation for this discipline, while on the other hand, it shows that many seemingly different applied many-dimensional systems (e.g., multi-agent systems, description logics with epistemic, temporal and dynamic operators, spatio-temporal logics, etc.) fit in perfectly with this theoretical framework, and so their computational behaviour can be analyzed using the developed machinery. We start with concrete examples of applied one- and many-dimensional modal logics such as temporal, epistemic, dynamic, description, spatial logics, and various combinations of these. Then we develop a mathematical theory for handling a spectrum of 'abstract' combinations of modal logics - fusions and products of modal logics, fragments of first-order modal and temporal logics - focusing on three major problems: decidability, axiomatizability, and computational complexity. Besides the standard methods of modal logic, the technical toolkit includes the method of quasimodels, mosaics, tilings, reductions to monadic second-order logic, algebraic logic techniques. Finally, we apply the developed machinery and obtained results to three case studies from the field of knowledge representation and reasoning: temporal epistemic logics for reasoning about multi-agent systems, modalized description logics for dynamic ontologies, and spatio-temporal logics. The genre of the book can be defined as a research monograph. It brings the reader to the front line of current research in the field by showing both recent achievements and directions of future investigations (in particular, multiple open problems). On the other hand, well-known results from modal and first-order logic are formulated without proofs and supplied with references to accessible sources. The intended audience of this book is logicians as well as those researchers who use logic in computer science and artificial intelligence. More specific application areas are, e.g., knowledge representation and reasoning, in particular, terminological, temporal and spatial reasoning, or reasoning about agents. And we also believe that researchers from certain other disciplines, say, temporal and spatial databases or geographical information systems, will benefit from this book as well. Key Features: Integrated approach to modern modal and temporal logics and their applications in artificial intelligence and computer science Written by internationally leading researchers in the field of pure and applied logic Combines mathematical theory of modal logic and applications in artificial intelligence and computer science Numerous open problems for further research Well illustrated with pictures and tables. (shrink)

Haḳdamah. Masekhet Taʻanit -- shel avotenu ṿe-shalanu -- Shaʻar 1. Ketsad medabrim ʻal birkat ha-ḥayim -- Shaʻar 2. Adam ṿe-adamah, ʻananim ṿe-heʻanut -- Shaʻar 3. ha-Homer ḥai u-medaber -- ha-ḥoḳ, ha-pele ṿeha-ʻanṿah -- Shaʻar 4. "Ka-mayim ha-panim la-panim ken lev ha-adam la-adam" -- normot ḥevratiyon u-reṿaḥat ha-adam -- Shaʻar 5. "Tefilah la-ʻani ki yaʻaṭof" -- ha-kisufim le-magaʻ -- Shaʻar 6. Nispaḥ ḥaṿayah ṿe-tiḳṿah.

In this paper I discuss card games designed to supplement or replace exercise sets on derivability and entailment in propositional logic. I present rules for two propositional logic card games that introduce chance and competition into discussions of propositional logic. The latter sections provide brief practical and theoretical notes on this kind of game, including ways courses that use these games can be more effective than courses that do not.

This essay evaluates the moral logic of ‘liberal eugenics’: the ideal of genetic control which leaves decisions about what sort of people to produce in the hands of individual parents, absent government intervention. I argue that liberal eugenics cannot be justified on the basis of the underlying liberal theory which inspires it. I introduce an alternative to Rawls's social primary goods that might be called natural primary goods: hereditable mental and physical capacities and dispositions that are valued across a range (...) of projects and pursuits. I suggest that reproductive genetic biotechnologies like embryo selection, cellular surgery, and genetic engineering, which aim to enhance ‘general purpose’ traits in offspring are less like childrearing practices a liberal government leaves to the discretion of parents than like practices the state makes compulsory. I argue that if the liberal commitment to autonomy is important enough for the state to mandate childrearing practices such as health care and basic education, that very same interest is important enough for the state to mandate safe, effective, and functionally integrated genetic practices that act on analogous all‐purpose traits such as resistance to disease and general cognitive functioning. I conclude that the liberal case for compulsory eugenics is a reductio against liberal theory. (shrink)

This paper is part of a research program centered around argumentation networks and offering several research directions for argumentation networks, with a view of using such networks for integrating logics and network reasoning. In Section 1 we introduce our program manifesto. In Section 2 we motivate and show how to substitute one argumentation network as a node in another argumentation network. Substitution is a purely logical operation and doing it for networks, besides developing their theory further, also helps us see (...) how to bring logic and networks closer together. Section 3 develops the formal properties of the new kind of network and Section 4 offers general discussion and comparison with the literature. (shrink)

In the biblical Book of Ruth, Boaz instructs his workers not to molest Ruth. We draw insights on the problem of workplace sexual harassment in the family-firm setting from the Book of Ruth. We then integrate these insights with several discrete findings in the literatures on workplace sexual harassment and family firms: First, family firms are relatively strong when it comes to a culture of fairness and respect. Second, family firms sometimes lack formal codes of ethics, which could hamper integrity. (...) Third, religious exemplars can reinforce the positive culture of family firms and even substitute for a formal code of ethics. Fourth, religious exemplars can also attenuate excessive risk-taking behavior in family firms. (shrink)

This Article considers the moral and legal status of practices that aim to modify traits in human offspring. As advancements in reproductive biotechnology give parents greater power to shape the genetic constitution of their children, an emerging school of legal scholars has ushered in a privatized paradigm of genetic control. Commentators defend a constitutionally protected right to prenatal engineering by appeal to the significance of procreative liberty and the promise of producing future generations who are more likely to have their (...) lives go well. This 'new eugenics,' however, confronts us with ethical challenges that neither liberal arguments about autonomy, fairness, and consent, nor utilitarian arguments about preferences, happiness, and equality, are able to capture. I begin by analyzing the Supreme Court's modern substantive due process jurisprudence, as it bears on recent advancements and controversies in genetic science. After developing a doctrinal framework that could support an asserted right to genetic engineering, I draw on empirical research in behavioral psychology to examine the influence of eugenic norms on egalitarian attitudes and institutions. I predict that if parents become accustomed to choosing the genes of their children, it would be radically more difficult to give an influential account for why the successful should adopt a charitable posture toward those who are less fortunate. I argue that by shifting control over offspring DNA from chance to choice, enhancement will inflate a sense of individual entitlement for social and economic outcomes. I conclude that increasing willingness to prevent the birth of abnormal children distracts attention from institutions that fail to accommodate the limitations of imperfect people. Some may reply that producing people who better fit the roles society chooses to reward need not deter us from providing for people whose abilities fail to meet the demands of modern society. However, this reply misses the way that changes in reproductive practices can bring about changes in the way that we understand our identities and relationships. Eugenic solutions to social problems such as poverty, crime, and unemployment reshape the challenge of genetic disadvantage so that it is no longer one we address through collective measures such as public education, social services, and income redistribution, and instead becomes one for individual parents to prevent through donor screening, embryo discard, or selective abortion. (shrink)

This much-needed book provides a thorough account of temporal logic, one of the most important areas of logic in computer science today. The book begins with a solid introduction to semantical and axiomatic approaches to temporal logic. It goes on to cover predicate temporal logic, meta-languages, general theories of axiomatization, many dimensional systems, propositional quantifiers, expressive power, Henkin dimension, temporalization of other logics, and decidability results. With its inclusion of cutting-edge results and unifying methodologies, this book is an indispensable reference (...) for both the pure logician and the theoretical computer scientist. (shrink)

The first edition of the Handbook of Philosophical Logic (four volumes) was published in the period 1983-1989 and has proven to be an invaluable reference work ...

In 2005 the author introduced networks which allow attacks on attacks of any level. So if a → b reads a attacks 6, then this attack can itself be attacked by another node c. This attack itself can attack another node d. This situation can be iterated to any level with attacks and nodes attacking other attacks and other nodes. In this paper we provide semantics to such networks. We offer three different approaches to obtaining semantics. 1. The translation approach (...) This uses the methodology of ' Logic by translation'. We translate faithfully the new networks into ordinary Dung networks with more nodes and extract the semantics from the translation. 2. The labelling approach This method regards the arrows as additional entities to be attacked and to mount attacks and applies a variation of the usual machinery of Camindada like labelling to the network. The new concept we need to employ here is that of 'joint attacks'. 3. The logic programming approach We translate the higher level network into a logic program and obtain semantics for it through known semantics for logic programs. We then compare our methods with those of S. Modgil and P. M. Dung et al. (shrink)

This book offers a systematic and critical discussion of Peter Winch's writings on the philosophy of the social sciences. The author points to Winch's tendency to over-emphasize the importance of language and communication, and his insufficient attention to the role of practical, technological activites in human life and society. It also offers an appendix devoted to the controversy between the anthropologists Marshall Sahlins and Gananath Obeyesekere regarding Captain James Cook's Hawaiian adventures. Essential reading for those studying the development of philosophy (...) in the twentieth century, this book will also be of great interest to anthropologists, sociologists, scholars of religion, and all those with an interest in the relationship between philosophy and the social sciences. (shrink)

Logics are like shadows on a wall; to understand why they dance as they do, and how they can be made to move differently, one needs to look at the mathematical structures from which they can be projected. That is a methodology that has long proven its value for classical and other forms of deductive inference; this book manifests its pertinence to logics of uncertain qualitative reasoning. It draws together and refines work from the literature on preferential and other quite (...) different semantics for such reasoning and then, in its central chapter, integrates the leading ideas from them into a single multi-dimensional semantics. It enters new territory with investigations of interpolation and qualitative independence in non-monotonic contexts as well as connections between non-monotonic logic and neuroscience, specifically with Edelman's theory of organization of the brain. Finally, it proposes novel applications such as equational modellings for contrary-to-duty normative reasoning and mathematical analyses of some kinds of casuistic reasoning in the Talmudic tradition. Profusely signposted at every turn, the volume is accessible to readers equipped with a modicum of set theory and abstract algebra. Visitors to the area can come in by the front gate and work their way, in various orders, through as much of the garden as strikes their fancy; specialists will enter at Chap. 11 or at whatever special topic interests them, well assured that they can easily backtrack to whatever bits and pieces are needed from what they skipped. A volume with a clear vision, a book to return to many times." (David Makinson). (shrink)